On infinite dimensional Ito’s formula
HTML articles powered by AMS MathViewer
- by T. F. Lin PDF
- Proc. Amer. Math. Soc. 49 (1975), 219-226 Request permission
Abstract:
Ito’s formula for $Y(t)g(t,\xi (t))$ is given where $g$ is a Hilbert space valued function, $\xi (t)$ is a diffusion on Hilbert space and $Y(t)$ is an operator-valued stochastic integral w.r.t. $\xi (t)$. A stochastic integral representation for solution of a certain second order parabolic equation is also given.References
- Ruth F. Curtain and Peter L. Falb, Ito’s lemma in infinite dimensions, J. Math. Anal. Appl. 31 (1970), 434–448. MR 261718, DOI 10.1016/0022-247X(70)90037-5
- J. Kuelbs, Gaussian measures on a Banach space, J. Functional Analysis 5 (1970), 354–367. MR 0260010, DOI 10.1016/0022-1236(70)90014-5
- Hui Hsiung Kuo, On operator-valued stochastic integrals, Bull. Amer. Math. Soc. 79 (1973), 207–210. MR 317405, DOI 10.1090/S0002-9904-1973-13156-8
- H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
- V. Sazonov, On characteristic functionals, Teor. Veroyatnost. i Primenen. 3 (1958), 201–205 (Russian, with English summary). MR 0098423
- Daniel W. Stroock, On certain systems of parabolic equations, Comm. Pure Appl. Math. 23 (1970), 447–457. MR 272075, DOI 10.1002/cpa.3160230313
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 219-226
- MSC: Primary 60H05; Secondary 60J60
- DOI: https://doi.org/10.1090/S0002-9939-1975-0380984-6
- MathSciNet review: 0380984